Supermatertismic temperaments
Supermatertismic rank-two temperaments temper out the supermatertismic comma, 52734375/52706752 = [-6 3 9 -7⟩ (lasepru-atritriyo), the amount by which a stack of one 5/4, three 16/15s and seven 7/5s falls short of four octaves.
Temperaments dicussed elsewhere include:
Vydubychi
- Main article: Vydubychi
Subgroup: 2.3.5.7
Comma list: 52734375/52706752, 2199023255552/2197176384375
Mapping: [⟨1 28 -53 -57], ⟨0 -53 111 120]]
Optimal tuning (CTE): ~2 = 1\1, ~10125/7168 = 598.0747
Optimal ET sequence: 311, 624, 935, 4986d, 5921d, 6856d, 7791bd, 8726bdd, 9661bdd
Badness: 0.156974
11-limit
Subgroup: 2.3.5.7.11
Comma list: 131072/130977, 151263/151250, 161280/161051
Mapping: [⟨1 28 -53 -57 -9], ⟨0 -53 111 120 25]]
Optimal tuning (CTE): ~2 = 1\1, ~847/600 = 598.0745
Optimal ET sequence: 311, 624, 935, 2181e, 3116ee
Badness: 0.066481
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 4096/4095, 91125/91091, 151263/151250
Mapping: [⟨1 28 -53 -57 -9 66], ⟨0 -53 111 120 25 -125]]
Optimal tuning (CTE): ~2 = 1\1, ~572/405 = 598.0747
Optimal ET sequence: 311, 624, 935
Badness: 0.033925
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 2058/2057, 2080/2079, 2500/2499, 4096/4095, 11016/11011
Mapping: [⟨1 28 -53 -57 -9 66 -124], ⟨0 -53 111 120 25 -125 257]]
Optimal tuning (CTE): ~2 = 1\1, ~544/385 = 598.0744
Optimal ET sequence: 311, 624, 935, 2181e
Badness: 0.023780
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3136/3135, 11016/11011
Mapping: [⟨1 28 -53 -57 -9 66 -124 -74], ⟨0 -53 111 120 25 -125 257 157]]
Optimal tuning (CTE): ~2 = 1\1, ~171/121 = 598.0742
Optimal ET sequence: 311, 624, 935, 1246e, 2181e
Badness: 0.015527
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 2025/2024, 2058/2057, 2080/2079, 2432/2431, 2500/2499, 3060/3059, 3520/3519
Mapping: [⟨1 28 -53 -57 -9 66 -124 -74 12], ⟨0 -53 111 120 25 -125 257 157 -15]]
Optimal tuning (CTE): ~2 = 1\1, ~171/121 = 598.0743
Optimal ET sequence: 311, 624, 935, 1246ei, 2181eii
Badness: 0.012821